Question

a line passes through the points (10, 8) and (2, 9). what is its equation in point - slope form? use one of the specified points in your equation. write your answer using integers, proper fractions, and improper fractions. simplify all fractions.

Explanation:

Step1: Calculate the slope

The slope $m$ between two points $(x_1,y_1)=(10,8)$ and $(x_2,y_2)=(2,9)$ is given by the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. So, $m=\frac{9 - 8}{2 - 10}=\frac{1}{-8}=-\frac{1}{8}$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(x_1,y_1)=(10,8)$ and $m =-\frac{1}{8}$, we get $y - 8=-\frac{1}{8}(x - 10)$.

Answer:

$y - 8=-\frac{1}{8}(x - 10)$